chiragr wrote:

At a certain department store present-wrapping counter, each clerk will wrap no fewer than twenty and no more than thirty presents per hour. If seventy people are standing in line, will all of their presents be wrapped after one hour?

(1) Each person in line has at least one present to be wrapped by one of the six clerks at the counter.

(2) If each person in line had one more present to be wrapped, nine clerks would be required to guarantee that every present would be wrapped in one hour.

Given: At a certain department store present-wrapping counter, each clerk will wrap no fewer than twenty and no more than thirty presents per hour. Target question: If seventy people are standing in line, will all of their presents be wrapped after one hour? Statement 1: Each person in line has at least one present to be wrapped by one of the six clerks at the counter. Since we aren't told the MAXIMUM number of presents each person has, there's no way to answer the target question.

To see what I mean, consider these two conflicting scenarios:

Case a: Each person in line has 1 present. So, there are 70 presents to be wrapped by 6 clerks. Since each clerk can wrap AT LEAST 20 presents (for a total of 120 presents), the answer to the target question is

YES, all of the presents will be wrapped after 1 hourCase b: Each person in line has 1 trillion presents. Here, the answer to the target question is

NO, all of the presents will NOT be wrapped after 1 hourSince we cannot answer the

target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: If each person in line had one more present to be wrapped, nine clerks would be required to guarantee that every present would be wrapped in one hour.Here, we aren't given any information about the actual number of clerks.

Consider these two conflicting scenarios:

Case a: There are 9 clerks available. If 9 clerks can wrap all of the presents in the hypothetical situation in which everyone has 1 EXTRA present, then 9 clerks will definitely be enough to wrap the presents. In other words, the answer to the target question is

YES, all of the presents will be wrapped after 1 hourCase b: There is are ZERO clerks available (all on lunch break). Here, the answer to the target question is

NO, all of the presents will NOT be wrapped after 1 hourSince we cannot answer the

target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined Let T = the TOTAL number of presents to be wrapped

IF each of the 70 people in line had one more present, then there WOULD be T + 70 presents to be wrapped

Since each of the 9 clerks can wrap AT LEAST 20 presents per hour, they can wrap AT LEAST 180 presents.

So, we can write:

T + 70 < 180Subtract 70 from both sides to get:

T < 110So, statement 2 is telling us (indirectly) that there are fewer than 110 presents to be wrapped

Statement 1 tells there are 6 clerks.

Since each clerk can wrap AT LEAST 20 presents in one hour, they can can wrap AT LEAST 120 presents in total.

Since statement 2 tells us that there are FEWER THAN 110 presents, the answer to the target question is

YES, all of the presents will be wrapped after 1 hourSince we can answer the

target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,

Brent

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